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666                           Ideal Diagrams.

gear, and the shaded portion indicates the change in lead value.
Decreasing towards the centre, it vanishes entirely at w, where the
opening is h w. At o v the throw is equal to the lap, and there-
fore the valve does not open at all at positions on the link
corresponding to between points v and s.

Space prevents us giving proof of the above, which, while
being only approximate, is quite near enough for practical
purposes. (See p. 1146.)

Ideal Indicator Diagrams for Compound Engines.
 We examined in Fig. 622 the form of diagram we should
expect to obtain from a single cylinder, and in Fig. 624 some
actual diagrams from a three-cylinder compound. The forms in
the latter case were sufficiently clear to shew considerable
difference of character over those taken from a single-cylinder
engine. We shall investigate the ideal diagrams for two-stage
compounds, believing that a careful examination will enable the
student to carry the method to three or four-stage compounds.
To simplify matters, we shall work with numbers instead of letters.
Naturally, in building up such diagrams, the only question we ask
from time to time, is, 'What is the change of pressure with a
particular change of volume ?' Two formulae are needed to meet
all cases.

(r) When the volume increases or decreases regularly within
the same vessel :

(2) When two or more vessels, having each a particular volume,
and each containing gas at a particular pressure, are
suddenly placed in communication :

P final

+   v   -1-  v

Also, for simplicity, the hyperbola is taken to represent the
relation of pressure and volume. See Fig. 620.

I. Tandem Engine^ with one cylinder behind the other, and
both pistons on one rod. Sketching the cylinders at A, Fig. 657,
we adopt the artifice of applying a i^ovable paper strip B to